Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach


In this paper, we show a branch-and-cut approach to solve the minimum spanning tree problem with conflicting edge pairs. This is a NP-hard variant of the classical minimum spanning tree problem, in which there are mutually exclusive edges. We introduce a new set of valid inequalities for the problem, based on the properties of its feasible solutions, and we develop a branch-and-cut algorithm based on them. Computational tests are performed both on benchmark instances coming from the literature and on some newly proposed ones. Results show that our approach outperforms a previous branch-and-cut algorithm proposed for the same problem.

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Correspondence to Rosa Pentangelo.

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Carrabs, F., Cerulli, R., Pentangelo, R. et al. Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach. Ann Oper Res 298, 65–78 (2021).

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  • Minimum spanning tree
  • Conflicting edges
  • Branch-and-cut